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<h1 align="center">Source for file QRDecomposition.php</h1>
<p>Documentation is available at <a href="../JAMA/_PHPExcel---Shared---JAMA---QRDecomposition.php.html">QRDecomposition.php</a></p>
<div class="src-code">
<ol><li><div class="src-line"><a name="a1"></a><span class="src-php">&lt;?php</span></div></li>
<li><div class="src-line"><a name="a2"></a><span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a3"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@package</span><span class="src-doc">&nbsp;JAMA</span></div></li>
<li><div class="src-line"><a name="a4"></a><span class="src-doc">&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a5"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For&nbsp;an&nbsp;m-by-n&nbsp;matrix&nbsp;A&nbsp;with&nbsp;m&nbsp;&gt;=&nbsp;n,&nbsp;the&nbsp;QR&nbsp;decomposition&nbsp;is&nbsp;an&nbsp;m-by-n</span></div></li>
<li><div class="src-line"><a name="a6"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;orthogonal&nbsp;matrix&nbsp;Q&nbsp;and&nbsp;an&nbsp;n-by-n&nbsp;upper&nbsp;triangular&nbsp;matrix&nbsp;R&nbsp;so&nbsp;that</span></div></li>
<li><div class="src-line"><a name="a7"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A&nbsp;=&nbsp;Q*R.</span></div></li>
<li><div class="src-line"><a name="a8"></a><span class="src-doc">&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a9"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The&nbsp;QR&nbsp;decompostion&nbsp;always&nbsp;exists,&nbsp;even&nbsp;if&nbsp;the&nbsp;matrix&nbsp;does&nbsp;not&nbsp;have</span></div></li>
<li><div class="src-line"><a name="a10"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;full&nbsp;rank,&nbsp;so&nbsp;the&nbsp;constructor&nbsp;will&nbsp;never&nbsp;fail.&nbsp;&nbsp;The&nbsp;primary&nbsp;use&nbsp;of&nbsp;the</span></div></li>
<li><div class="src-line"><a name="a11"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;QR&nbsp;decomposition&nbsp;is&nbsp;in&nbsp;the&nbsp;least&nbsp;squares&nbsp;solution&nbsp;of&nbsp;nonsquare&nbsp;systems</span></div></li>
<li><div class="src-line"><a name="a12"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;of&nbsp;simultaneous&nbsp;linear&nbsp;equations.&nbsp;&nbsp;This&nbsp;will&nbsp;fail&nbsp;if&nbsp;isFullRank()</span></div></li>
<li><div class="src-line"><a name="a13"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;returns&nbsp;false.</span></div></li>
<li><div class="src-line"><a name="a14"></a><span class="src-doc">&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a15"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@author</span><span class="src-doc">&nbsp;&nbsp;Paul&nbsp;Meagher</span></div></li>
<li><div class="src-line"><a name="a16"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@license</span><span class="src-doc">&nbsp;PHP&nbsp;v3.0</span></div></li>
<li><div class="src-line"><a name="a17"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@version</span><span class="src-doc">&nbsp;1.1</span></div></li>
<li><div class="src-line"><a name="a18"></a><span class="src-doc">&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a19"></a><span class="src-key">class&nbsp;</span><a href="../JAMA/PHPExcel_Shared_JAMA_QRDecomposition.html">PHPExcel_Shared_JAMA_QRDecomposition</a>&nbsp;<span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a20"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a21"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">const&nbsp;</span><span class="src-id">MatrixRankException&nbsp;&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-str">&quot;Can&nbsp;only&nbsp;perform&nbsp;operation&nbsp;on&nbsp;full-rank&nbsp;matrix.&quot;</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a22"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a23"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a24"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Array&nbsp;for&nbsp;internal&nbsp;storage&nbsp;of&nbsp;decomposition.</span></div></li>
<li><div class="src-line"><a name="a25"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">array&nbsp;</span></div></li>
<li><div class="src-line"><a name="a26"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a27"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$QR&nbsp;</span>=&nbsp;<span class="src-key">array</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a28"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a29"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a30"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Row&nbsp;dimension.</span></div></li>
<li><div class="src-line"><a name="a31"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">integer&nbsp;</span></div></li>
<li><div class="src-line"><a name="a32"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a33"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$m</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a34"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a35"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a36"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Column&nbsp;dimension.</span></div></li>
<li><div class="src-line"><a name="a37"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">integer&nbsp;</span></div></li>
<li><div class="src-line"><a name="a38"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a39"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$n</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a40"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a41"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a42"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Array&nbsp;for&nbsp;internal&nbsp;storage&nbsp;of&nbsp;diagonal&nbsp;of&nbsp;R.</span></div></li>
<li><div class="src-line"><a name="a43"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc">&nbsp;</span><span class="src-doc-type">array&nbsp;</span></div></li>
<li><div class="src-line"><a name="a44"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a45"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$Rdiag&nbsp;</span>=&nbsp;<span class="src-key">array</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a46"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a47"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a48"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a49"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;QR&nbsp;Decomposition&nbsp;computed&nbsp;by&nbsp;Householder&nbsp;reflections.</span></div></li>
<li><div class="src-line"><a name="a50"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a51"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@param&nbsp;</span><span class="src-doc-type">matrix&nbsp;</span><span class="src-doc-var">$A&nbsp;</span><span class="src-doc">Rectangular&nbsp;matrix</span></div></li>
<li><div class="src-line"><a name="a52"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">Structure&nbsp;</span><span class="src-doc">to&nbsp;access&nbsp;R&nbsp;and&nbsp;the&nbsp;Householder&nbsp;vectors&nbsp;and&nbsp;compute&nbsp;Q.</span></div></li>
<li><div class="src-line"><a name="a53"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a54"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/PHPExcel_Shared_JAMA_QRDecomposition.html#method__construct">__construct</a><span class="src-sym">(</span><span class="src-var">$A</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a55"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if</span><span class="src-sym">(</span><span class="src-var">$A&nbsp;</span>instanceof&nbsp;<span class="src-id"><a href="../JAMA/PHPExcel_Shared_JAMA_Matrix.html">PHPExcel_Shared_JAMA_Matrix</a></span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a56"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Initialize.</span></div></li>
<li><div class="src-line"><a name="a57"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR&nbsp;</span>=&nbsp;<span class="src-var">$A</span><span class="src-sym">-&gt;</span><span class="src-id">getArrayCopy</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a58"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$A</span><span class="src-sym">-&gt;</span><span class="src-id">getRowDimension</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a59"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$A</span><span class="src-sym">-&gt;</span><span class="src-id">getColumnDimension</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a60"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Main&nbsp;loop.</span></div></li>
<li><div class="src-line"><a name="a61"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a62"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Compute&nbsp;2-norm&nbsp;of&nbsp;k-th&nbsp;column&nbsp;without&nbsp;under/overflow.</span></div></li>
<li><div class="src-line"><a name="a63"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$nrm&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a64"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a65"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$nrm&nbsp;</span>=&nbsp;<a href="../JAMA/_PHPExcel---Shared---JAMA---utils---Maths.php.html#functionhypo">hypo</a><span class="src-sym">(</span><span class="src-var">$nrm</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a66"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a67"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$nrm&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a68"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Form&nbsp;k-th&nbsp;Householder&nbsp;vector.</span></div></li>
<li><div class="src-line"><a name="a69"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>&lt;&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a70"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$nrm&nbsp;</span>=&nbsp;-<span class="src-var">$nrm</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a71"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a72"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a73"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>/=&nbsp;<span class="src-var">$nrm</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a74"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a75"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-num">1.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a76"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Apply&nbsp;transformation&nbsp;to&nbsp;remaining&nbsp;columns.</span></div></li>
<li><div class="src-line"><a name="a77"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a78"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a79"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a80"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a81"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a82"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;-<span class="src-var">$s</span>/<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a83"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a84"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a85"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a86"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a87"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a88"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">Rdiag</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$nrm</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a89"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a90"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a91"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;throw&nbsp;<span class="src-key">new&nbsp;</span><span class="src-id">Exception</span><span class="src-sym">(</span><span class="src-id"><a href="../JAMA/PHPExcel_Shared_JAMA_Matrix.html">PHPExcel_Shared_JAMA_Matrix</a></span><span class="src-sym">::</span><span class="src-id">ArgumentTypeException</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a92"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a93"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;&nbsp;&nbsp;&nbsp;function&nbsp;__construct()</span></div></li>
<li><div class="src-line"><a name="a94"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a95"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a96"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a97"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Is&nbsp;the&nbsp;matrix&nbsp;full&nbsp;rank?</span></div></li>
<li><div class="src-line"><a name="a98"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a99"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">boolean&nbsp;</span><span class="src-doc">true&nbsp;if&nbsp;R,&nbsp;and&nbsp;hence&nbsp;A,&nbsp;has&nbsp;full&nbsp;rank,&nbsp;else&nbsp;false.</span></div></li>
<li><div class="src-line"><a name="a100"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a101"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/PHPExcel_Shared_JAMA_QRDecomposition.html#methodisFullRank">isFullRank</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a102"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a103"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">Rdiag</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>==&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a104"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-id">false</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a105"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a106"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a107"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-id">true</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a108"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;&nbsp;&nbsp;&nbsp;function&nbsp;isFullRank()</span></div></li>
<li><div class="src-line"><a name="a109"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a110"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a111"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a112"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Return&nbsp;the&nbsp;Householder&nbsp;vectors</span></div></li>
<li><div class="src-line"><a name="a113"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a114"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">Matrix&nbsp;</span><span class="src-doc">Lower&nbsp;trapezoidal&nbsp;matrix&nbsp;whose&nbsp;columns&nbsp;define&nbsp;the&nbsp;reflections</span></div></li>
<li><div class="src-line"><a name="a115"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a116"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/PHPExcel_Shared_JAMA_QRDecomposition.html#methodgetH">getH</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a117"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a118"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a119"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>&gt;=&nbsp;<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a120"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a121"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a122"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a123"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a124"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a125"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a126"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-key">new&nbsp;</span><span class="src-id"><a href="../JAMA/PHPExcel_Shared_JAMA_Matrix.html">PHPExcel_Shared_JAMA_Matrix</a></span><span class="src-sym">(</span><span class="src-var">$H</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a127"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;&nbsp;&nbsp;&nbsp;function&nbsp;getH()</span></div></li>
<li><div class="src-line"><a name="a128"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a129"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a130"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a131"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Return&nbsp;the&nbsp;upper&nbsp;triangular&nbsp;factor</span></div></li>
<li><div class="src-line"><a name="a132"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a133"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">Matrix&nbsp;</span><span class="src-doc">upper&nbsp;triangular&nbsp;factor</span></div></li>
<li><div class="src-line"><a name="a134"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a135"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/PHPExcel_Shared_JAMA_QRDecomposition.html#methodgetR">getR</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a136"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a137"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a138"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a139"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$R</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a140"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">elseif&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>==&nbsp;<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a141"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$R</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">Rdiag</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a142"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a143"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$R</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a144"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a145"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a146"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a147"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-key">new&nbsp;</span><span class="src-id"><a href="../JAMA/PHPExcel_Shared_JAMA_Matrix.html">PHPExcel_Shared_JAMA_Matrix</a></span><span class="src-sym">(</span><span class="src-var">$R</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a148"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;&nbsp;&nbsp;&nbsp;function&nbsp;getR()</span></div></li>
<li><div class="src-line"><a name="a149"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a150"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a151"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a152"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Generate&nbsp;and&nbsp;return&nbsp;the&nbsp;(economy-sized)&nbsp;orthogonal&nbsp;factor</span></div></li>
<li><div class="src-line"><a name="a153"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a154"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">Matrix&nbsp;</span><span class="src-doc">orthogonal&nbsp;factor</span></div></li>
<li><div class="src-line"><a name="a155"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a156"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/PHPExcel_Shared_JAMA_QRDecomposition.html#methodgetQ">getQ</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a157"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&gt;=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a158"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a159"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$Q</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a160"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a161"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$Q</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">1.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a162"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a163"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>!=&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a164"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a165"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a166"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$Q</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a167"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a168"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;-<span class="src-var">$s</span>/<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a169"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a170"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$Q</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a171"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a172"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a173"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a174"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a175"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">/*</span></div></li>
<li><div class="src-line"><a name="a176"></a><span class="src-comm">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for($i&nbsp;=&nbsp;0;&nbsp;$i&nbsp;&lt;&nbsp;count($Q);&nbsp;++$i)&nbsp;{</span></div></li>
<li><div class="src-line"><a name="a177"></a><span class="src-comm">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for($j&nbsp;=&nbsp;0;&nbsp;$j&nbsp;&lt;&nbsp;count($Q);&nbsp;++$j)&nbsp;{</span></div></li>
<li><div class="src-line"><a name="a178"></a><span class="src-comm">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if(!&nbsp;isset($Q[$i][$j])&nbsp;)&nbsp;{</span></div></li>
<li><div class="src-line"><a name="a179"></a><span class="src-comm">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$Q[$i][$j]&nbsp;=&nbsp;0;</span></div></li>
<li><div class="src-line"><a name="a180"></a><span class="src-comm">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;}</span></div></li>
<li><div class="src-line"><a name="a181"></a><span class="src-comm">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;}</span></div></li>
<li><div class="src-line"><a name="a182"></a><span class="src-comm">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;}</span></div></li>
<li><div class="src-line"><a name="a183"></a><span class="src-comm">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a184"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-key">new&nbsp;</span><span class="src-id"><a href="../JAMA/PHPExcel_Shared_JAMA_Matrix.html">PHPExcel_Shared_JAMA_Matrix</a></span><span class="src-sym">(</span><span class="src-var">$Q</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a185"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;&nbsp;&nbsp;&nbsp;function&nbsp;getQ()</span></div></li>
<li><div class="src-line"><a name="a186"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a187"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a188"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a189"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Least&nbsp;squares&nbsp;solution&nbsp;of&nbsp;A*X&nbsp;=&nbsp;B</span></div></li>
<li><div class="src-line"><a name="a190"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a191"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@param&nbsp;</span><span class="src-doc-type">Matrix&nbsp;</span><span class="src-doc-var">$B&nbsp;</span><span class="src-doc">A&nbsp;Matrix&nbsp;with&nbsp;as&nbsp;many&nbsp;rows&nbsp;as&nbsp;A&nbsp;and&nbsp;any&nbsp;number&nbsp;of&nbsp;columns.</span></div></li>
<li><div class="src-line"><a name="a192"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">Matrix&nbsp;</span><span class="src-doc">Matrix&nbsp;that&nbsp;minimizes&nbsp;the&nbsp;two&nbsp;norm&nbsp;of&nbsp;Q*R*X-B.</span></div></li>
<li><div class="src-line"><a name="a193"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a194"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/PHPExcel_Shared_JAMA_QRDecomposition.html#methodsolve">solve</a><span class="src-sym">(</span><span class="src-var">$B</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a195"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$B</span><span class="src-sym">-&gt;</span><span class="src-id">getRowDimension</span><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span>==&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a196"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><a href="../JAMA/PHPExcel_Shared_JAMA_QRDecomposition.html#methodisFullRank">isFullRank</a><span class="src-sym">(</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a197"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Copy&nbsp;right&nbsp;hand&nbsp;side</span></div></li>
<li><div class="src-line"><a name="a198"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$nx&nbsp;</span>=&nbsp;<span class="src-var">$B</span><span class="src-sym">-&gt;</span><span class="src-id">getColumnDimension</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a199"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$X&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$B</span><span class="src-sym">-&gt;</span><span class="src-id">getArrayCopy</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a200"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Compute&nbsp;Y&nbsp;=&nbsp;transpose(Q)*B</span></div></li>
<li><div class="src-line"><a name="a201"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a202"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$nx</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a203"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a204"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a205"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$X</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a206"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a207"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;-<span class="src-var">$s</span>/<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a208"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a209"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$X</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a210"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a211"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a212"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a213"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Solve&nbsp;R*X&nbsp;=&nbsp;Y;</span></div></li>
<li><div class="src-line"><a name="a214"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&gt;=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a215"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$nx</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a216"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$X</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>/=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">Rdiag</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a217"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a218"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a219"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$nx</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a220"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$X</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>-=&nbsp;<span class="src-var">$X</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">QR</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a221"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a222"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a223"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a224"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$X&nbsp;</span>=&nbsp;<span class="src-key">new&nbsp;</span><span class="src-id"><a href="../JAMA/PHPExcel_Shared_JAMA_Matrix.html">PHPExcel_Shared_JAMA_Matrix</a></span><span class="src-sym">(</span><span class="src-var">$X</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a225"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-sym">(</span><span class="src-var">$X</span><span class="src-sym">-&gt;</span><span class="src-id">getMatrix</span><span class="src-sym">(</span><span class="src-num">0</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">,&nbsp;</span><span class="src-num">0</span><span class="src-sym">,&nbsp;</span><span class="src-var">$nx</span><span class="src-sym">))</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a226"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a227"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;throw&nbsp;<span class="src-key">new&nbsp;</span><span class="src-id">Exception</span><span class="src-sym">(</span><span class="src-id">self</span><span class="src-sym">::</span><span class="src-id">MatrixRankException</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a228"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a229"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a230"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;throw&nbsp;<span class="src-key">new&nbsp;</span><span class="src-id">Exception</span><span class="src-sym">(</span><span class="src-id"><a href="../JAMA/PHPExcel_Shared_JAMA_Matrix.html">PHPExcel_Shared_JAMA_Matrix</a></span><span class="src-sym">::</span><span class="src-id">MatrixDimensionException</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a231"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a232"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;&nbsp;&nbsp;&nbsp;function&nbsp;solve()</span></div></li>
<li><div class="src-line"><a name="a233"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a234"></a><span class="src-sym">}&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;&nbsp;&nbsp;&nbsp;PHPExcel_Shared_JAMA_class&nbsp;QRDecomposition</span></div></li>
</ol>
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		    Documentation generated on Fri, 12 Oct 2012 00:17:33 +0200 by <a href="http://www.phpdoc.org">phpDocumentor 1.4.4</a>
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